Abstract
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of d, N × N matrices invariant under the adjoint action of the symmetric group SN. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group.
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Acknowledgments
DO’C is supported by the Irish Research Council and Science Foundation Ireland under grant SFI-IRC-21/PATH-S/9391. SR is supported by the Science and Technology Facilities Council (STFC) Consolidated Grants ST/P000754/1 “String theory, gauge theory and duality” and ST/T000686/1 “Amplitudes, strings and duality”. SR thanks the Dublin Institute for Advanced Studies for hospitality while part of this work was being done. We thank Yuhma Asano, George Barnes, Samuel Kováçik, Veselin Filev and Adrian Padellaro for discussions related to the subject of this paper.
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O’Connor, D., Ramgoolam, S. Gauged permutation invariant matrix quantum mechanics: path integrals. J. High Energ. Phys. 2024, 80 (2024). https://doi.org/10.1007/JHEP04(2024)080
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DOI: https://doi.org/10.1007/JHEP04(2024)080